Israel Journal of Mathematics

, Volume 86, Issue 1, pp 253–275

Piecewise-polynomial approximation of functions fromH((0, 1)d), 2ℓ=d, and applications to the spectral theory of the Schrödinger operator

  • M. Solomyak

DOI: 10.1007/BF02773681

Cite this article as:
Solomyak, M. Israel J. Math. (1994) 86: 253. doi:10.1007/BF02773681


For the selfadjoint Schrödinger operator −Δ−αV on ℝ2 the number of negative eigenvalues is estimated. The estimates obtained are based upon a new result on the weightedL2-approximation of functions from the Sobolev spaces in the cases corresponding to the critical exponent in the embedding theorem.

Copyright information

© The Magnes Press 1994

Authors and Affiliations

  • M. Solomyak
    • 1
  1. 1.Department of Theoretical MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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